You don't need a new travel day if you stay on the same train after midnight. Your journey would count as 2 travel days because you change to another train after midnight.

On what date is that? There should be a direct night train Munich - Amsterdam, usually leaving around 22:50, for which you only need 1 travel day and a reservation (14€ for a seat).

OR-for ´free´ in 1 day (assuming you do not need using trains that day before) the ICE 618 starts from M @0.01 and runs via the Ruhr area (Köln-Düsseldorf-Duisburg), where in all you can change into the ICE to AMS. Duisburg has the dubious honor of being since many years the worst of the worst, most neglected of all Germanyś big main stations. K has the best variety of shops and food, also open early morning. These trains are normal daytime ICE and have seats only. They mainly serve FRA-airport for early flyers.

Hello, by the night train you suggest, its the Nightjet NJ420? I have a question since im a foreing traveler from america, That train starts on innsburck and has a lot of stops, and one of them is munich in which has the time departure you refer 22:50, my question or doubt is, If I reserved a ticket to this NJ420 train, I can take it in munich without the need to take it on Innsburck? The Stops on the night trains route can be use to get off and board the train? thats my main question, since if that is possible I can plan my intinerary best.

@Giampiero Bonfiglioli

I saw in your profile that you plan to travel with the German Rail Pass. With that you can't go to Amsterdam. At least not according to the information on the Interrail website. 

https://www.interrail.eu/en/interrail-passes/german-rail-pass

But maybe you decided to buy a Global Pass instead of the German Rail Pass.

Yes, that's (Innsbruck - ) Munich - Amsterdam.

You can board it in Innsbruck or in Munich and in any of the other advertised stops in the evening. It's best to actually book the reservation from the stop where you intend to board.